Is a particle an irreducible representation of the Poincaré group?
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929525558870016 |
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| author | Caulton, Adam |
| author_facet | Caulton, Adam |
| contents | The claim that a particle is an irreducible representation of the Poincaré group -- what I call \emph{Wigner's identification} -- is now, decades on from Wigner's (1939) original paper, so much a part of particle physics folklore that it is often taken as, or claimed to be, a definition. My aims in this paper are to: (i) clarify, and partially defend, the guiding ideas behind this identification; (ii) raise objections to its being an adequate definition; and (iii) offer a rival characterisation of particles. My main objections to Wigner's identification appeal to the problem of interacting particles, and to alternative spacetimes. I argue that the link implied in Wigner's identification, between a spacetime's symmetries and the generator of a particle's space of states, is at best misleading, and that there is no good reason to link the generator of a particle's space of states to symmetries of any kind. I propose an alternative characterisation of particles, which captures both the relativistic and non-relativistic setting. I further defend this proposal by appeal to a theorem which links the decomposition of Poincaré generators into purely orbital and spin components with canonical algebraic relations between position, momentum and spin. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_02354 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Is a particle an irreducible representation of the Poincaré group? Caulton, Adam Quantum Physics History and Philosophy of Physics The claim that a particle is an irreducible representation of the Poincaré group -- what I call \emph{Wigner's identification} -- is now, decades on from Wigner's (1939) original paper, so much a part of particle physics folklore that it is often taken as, or claimed to be, a definition. My aims in this paper are to: (i) clarify, and partially defend, the guiding ideas behind this identification; (ii) raise objections to its being an adequate definition; and (iii) offer a rival characterisation of particles. My main objections to Wigner's identification appeal to the problem of interacting particles, and to alternative spacetimes. I argue that the link implied in Wigner's identification, between a spacetime's symmetries and the generator of a particle's space of states, is at best misleading, and that there is no good reason to link the generator of a particle's space of states to symmetries of any kind. I propose an alternative characterisation of particles, which captures both the relativistic and non-relativistic setting. I further defend this proposal by appeal to a theorem which links the decomposition of Poincaré generators into purely orbital and spin components with canonical algebraic relations between position, momentum and spin. |
| title | Is a particle an irreducible representation of the Poincaré group? |
| topic | Quantum Physics History and Philosophy of Physics |
| url | https://arxiv.org/abs/2410.02354 |